Short Answer 
The process to solve the logarithmic equation starts by rearranging it to log2x – log2(3x+5) = 4, applying the properties of logarithms to get log(2x / (3x + 5)) = 4, and finally converting to base form resulting in 10^4 = (2x / (3x + 5)), which leads to a solution of x approximately equal to 1.667.
Step 1: Rearranging the Equation
To begin with, we need to simplify the given logarithmic equation. This involves transposing the term log2(3x+5) to the other side. The new equation becomes:
- log2x – log2(3x+5) = 4
Step 2: Applying Logarithm Properties
Next, we apply the properties of logarithms to simplify the equation further. This is done using the quotient rule, which allows us to express it as:
- log(2x / (3x + 5)) = 4
Step 3: Converting to Base Form and Solving
The final step involves converting the logarithmic equation into base form. This means we express the equation as:
- 10^4 = (2x / (3x + 5))
After rearranging and solving this equation, we find that the value of x is approximately 1.667.